"use strict"; const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = { a: "a", annotation: "annotation", blockquote: "blockquote", br: "br", code: "code", del: "del", em: "em", h1: "h1", h2: "h2", h3: "h3", img: "img", li: "li", math: "math", mfrac: "mfrac", mi: "mi", mn: "mn", mo: "mo", mrow: "mrow", msub: "msub", ol: "ol", p: "p", path: "path", pre: "pre", semantics: "semantics", span: "span", strong: "strong", svg: "svg", ul: "ul", ..._provideComponents(), ...props.components }; return _jsxs(_Fragment, { children: [_jsxs(_components.h1, { id: "广义线性混合模型-glmm", children: [_jsx(_components.a, { className: "heading-link", href: "#广义线性混合模型-glmm", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "广义线性混合模型 (", _jsx(_components.em, { children: "GLMM" }), ")"] }), "\n", _jsxs(_components.h2, { id: "统计学知识", children: [_jsx(_components.a, { className: "heading-link", href: "#统计学知识", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "统计学知识"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.strong, { children: "“混合”" }), " 一词指的是除了回归分析的通常固定效应之外的随机效应。"] }), "\n", _jsxs(_components.ul, { children: ["\n", _jsx(_components.li, { children: "固定效应（fixed effect, FE）" }), "\n", _jsx(_components.li, { children: "随机效应（random effect, RE）" }), "\n"] }), "\n", _jsx(_components.p, { children: "固定效应和随机效应的区别就在于如何看待参数。" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsx(_components.li, { children: "对于固定效应来说，参数变化，引起应变量平均变化。" }), "\n", _jsx(_components.li, { children: "对于随机效应而言，参数是服从正态分布的一个随机变量，也就是说对于两个相同自变量，对应变量的影响不一定是相同的。" }), "\n"] }), "\n", _jsx(_components.p, { children: "对于固定部分我们得到的是模型参数的点估计，对于随机部分我们得到的是其概率分布。" }), "\n", _jsx(_components.img, { src: "https://dg-of-obsidain-cafwell.flowershow.me/FE%20and%20RE.png", alt: "FE and RE", className: "internal new" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["普通线性模型（以只有一个因变量举例）：", _jsx(_components.br, {}), "\n", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "y" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "0" })] }), _jsx(_components.mo, { children: "+" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.mo, { children: "∗" }), _jsx(_components.mi, { children: "x" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { children: "ε" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "y = \\beta_0 +\\beta_1 * x + ε" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.625em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0359em" }, children: "y" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "0" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "∗" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "ε" })] })] })] }), "\n或", _jsx(_components.br, {}), "\n", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "Y" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mi, { children: "β" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { children: "ε" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "Y=\\mathbf X\\beta + ε" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.2222em" }, children: "Y" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "ε" })] })] })] }), "\n也就是", _jsx(_components.strong, { children: "固定效应 + 随机误差" }), "，且因变量必须要满足", _jsx(_components.strong, { children: "正态性、独立性以及方差齐性" }), "。"] }), "\n"] }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["而广义线性模型（GLM）可以为：\n", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "l" }), _jsx(_components.mi, { children: "o" }), _jsx(_components.mi, { children: "g" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "P" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "y" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mn, { children: "1" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsxs(_components.mrow, { children: [_jsx(_components.mn, { children: "1" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "P" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "y" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mn, { children: "1" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] })] }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "0" })] }), _jsx(_components.mo, { children: "+" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.mo, { children: "∗" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "x" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { children: "ε" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "log(\\frac{P(y=1)}{1-P(y=1)})=\\beta_0 + \\beta_1 * x_1+ ε" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.53em", verticalAlign: "-0.52em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0197em" }, children: "l" }), _jsx(_components.span, { className: "mord mathnormal", children: "o" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0359em" }, children: "g" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.01em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "1" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.1389em" }, children: "P" }), _jsx(_components.span, { className: "mopen mtight", children: "(" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0359em" }, children: "y" }), _jsx(_components.span, { className: "mrel mtight", children: "=" }), _jsx(_components.span, { className: "mord mtight", children: "1" }), _jsx(_components.span, { className: "mclose mtight", children: ")" })] }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.485em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.1389em" }, children: "P" }), _jsx(_components.span, { className: "mopen mtight", children: "(" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.0359em" }, children: "y" }), _jsx(_components.span, { className: "mrel mtight", children: "=" }), _jsx(_components.span, { className: "mord mtight", children: "1" }), _jsx(_components.span, { className: "mclose mtight", children: ")" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.52em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "0" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "∗" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7333em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "ε" })] })] })] }), "\n或\n", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "l" }), _jsx(_components.mi, { children: "o" }), _jsx(_components.mi, { children: "g" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "y" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "0" })] }), _jsx(_components.mo, { children: "+" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.mo, { children: "∗" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "x" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { children: "ε" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "log(y) = \\beta_0 + \\beta_1 * x_1+ ε" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0197em" }, children: "l" }), _jsx(_components.span, { className: "mord mathnormal", children: "o" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0359em" }, children: "g" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0359em" }, children: "y" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "0" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "∗" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7333em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "ε" })] })] })] })] }), "\n"] }), "\n", _jsx(_components.p, { children: "GLM 之所以称为 “广义”，关键就在于这种变换 —— 连接函数（就是上边两个等式左边），使得模型的应用范围变得更宽，只要因变量服从指数分布就行；" }), "\n", _jsxs(_components.p, { children: ["线性混合模型（LMM）则形如（以矩阵形式表示）：\n", _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "Y" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mi, { children: "β" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { mathvariant: "bold", children: "Z" }), _jsx(_components.mi, { children: "γ" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { children: "ε" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "Y = \\mathbf X\\beta + \\mathbf Z \\gamma + ε" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.2222em" }, children: "Y" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0528em" }, children: "β" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8805em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", children: "Z" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.0556em" }, children: "γ" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "ε" })] })] })] })] }), "\n", _jsxs(_components.p, { children: ["相较普通线性模型，LMM 其实就是多了随机效应", _jsx(_components.em, { children: "Zγ" }), " ！"] }), "\n", _jsxs(_components.h3, { id: "什么时候用-glmm", children: [_jsx(_components.a, { className: "heading-link", href: "#什么时候用-glmm", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "什么时候用 GLMM"] }), "\n", _jsxs(_components.ol, { children: ["\n", _jsx(_components.li, { children: "适用于层级，多水平数据；" }), "\n", _jsx(_components.li, { children: "重复测量，非独立，或时间 - 空间的数据" }), "\n"] }), "\n", _jsxs(_components.h3, { id: "随机的类型", children: [_jsx(_components.a, { className: "heading-link", href: "#随机的类型", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "随机的类型"] }), "\n", _jsxs(_components.p, { children: ["随机效应有两种：", _jsx(_components.br, {}), "\n", "随机斜率 -", _jsx(_components.br, {}), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Coding/random-slopes.png", alt: "random-slopes|350", className: "internal" })] }), "\n", _jsxs(_components.p, { children: ["随机截距 -", _jsx(_components.br, {}), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Coding/random-intercepts.png", alt: "random-intercepts|350", className: "internal" })] }), "\n", _jsxs(_components.h3, { id: "随机部分的写法", children: [_jsx(_components.a, { className: "heading-link", href: "#随机部分的写法", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "随机部分的写法"] }), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Coding/random_of_glmm.png", alt: "random_of_glmm|600", className: "internal" }), "\n", _jsx(_components.p, { children: "一般是一和五两种写法，例：" }), "\n", _jsxs(_components.blockquote, { children: ["\n", _jsxs(_components.p, { children: ["wear", _jsx(_components.del, { children: "wheel+(1|car_type)\nwear" }), "wheel+(wheel|car_type)"] }), "\n"] }), "\n", _jsxs(_components.ul, { children: ["\n", _jsx(_components.li, { children: "前者意义是提供随机斜率；另一种意义是提供随机斜率和随机截距。" }), "\n", _jsx(_components.li, { children: "可以简单的把 \"（）\" 内的内容看为随机部分，\"（）\" 前面的是固定部分。随机部分 \"|\" 左边的提供随机斜率，左边写 1 即没有随机斜率，右边提供随机截距" }), "\n", _jsx(_components.li, { children: "后者中，\"|\" 左边的预测变量，必须也在固定部分出现" }), "\n"] }), "\n", _jsxs(_components.h3, { id: "嵌套交叉", children: [_jsx(_components.a, { className: "heading-link", href: "#嵌套交叉", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "嵌套；交叉"] }), "\n", _jsx(_components.p, { children: "数据可能有一个或多个聚类来源，而且聚类可能是分层的，比如聚类是嵌套在其他聚类中。一个例子是对学生进行多次的学术能力测试（重复观察嵌套在学生中，学生嵌套在学校中，学校嵌套在地区中）。" }), "\n", _jsx(_components.p, { children: "在其他情况下，不存在嵌套结构。一个例子是反应时间实验，参与者执行同一组任务。虽然观察结果是在个人内部嵌套的，但观察结果也是根据任务类型进行聚类的。" }), "\n", _jsxs(_components.p, { children: ["可以用", _jsx(_components.code, { className: "language-auto", children: "嵌套 (Nested)" }), "和", _jsx(_components.code, { className: "language-auto", children: "交叉 (Crossed)" }), "这两个术语来区分这些情况。此外，聚类可能是平衡的或不平衡的。"] }), "\n", _jsxs(_components.p, { children: ["嵌套图例：", _jsx(_components.br, {}), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Coding/Nested.png", alt: "plot_1|600", className: "internal" })] }), "\n", _jsxs(_components.p, { children: ["交叉：", _jsx(_components.br, {}), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Coding/Crossed.png", alt: "Crossed|500", className: "internal" })] }), "\n", _jsxs(_components.h2, { id: "r语言", children: [_jsx(_components.a, { className: "heading-link", href: "#r语言", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "R语言"] }), "\n", _jsx(_components.p, { children: "仍以实验数据为分析材料" }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["library", _jsx(_components.span, { className: "token punctuation", children: "(" }), "vroom", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["ball ", _jsx(_components.span, { className: "token operator", children: "<-" }), " vroom", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "\"https://raw.githubusercontent.com/ExperimentalConservation/Bioinformatics_data/master/IBT/all_groups_data.csv\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["ball", _jsx(_components.span, { className: "token operator", children: "$" }), "Species", _jsx(_components.span, { className: "token punctuation", children: "[" }), "which", _jsx(_components.span, { className: "token punctuation", children: "(" }), "ball", _jsx(_components.span, { className: "token operator", children: "$" }), "Species ", _jsx(_components.span, { className: "token operator", children: "==" }), " ", _jsx(_components.span, { className: "token string", children: "\"dark pink\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "<-" }), " ", _jsx(_components.span, { className: "token string", children: "\"darkpink\"" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["ball", _jsx(_components.span, { className: "token operator", children: "$" }), "Species", _jsx(_components.span, { className: "token punctuation", children: "[" }), "which", _jsx(_components.span, { className: "token punctuation", children: "(" }), "ball", _jsx(_components.span, { className: "token operator", children: "$" }), "Species ", _jsx(_components.span, { className: "token operator", children: "==" }), " ", _jsx(_components.span, { className: "token string", children: "\"darkgreen\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "<-" }), " ", _jsx(_components.span, { className: "token string", children: "\"teal\"" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["ball", _jsx(_components.span, { className: "token operator", children: "$" }), "Species", _jsx(_components.span, { className: "token punctuation", children: "[" }), "which", _jsx(_components.span, { className: "token punctuation", children: "(" }), "ball", _jsx(_components.span, { className: "token operator", children: "$" }), "Species ", _jsx(_components.span, { className: "token operator", children: "==" }), " ", _jsx(_components.span, { className: "token string", children: "\"lightgreen\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "]" }), " ", _jsx(_components.span, { className: "token operator", children: "<-" }), " ", _jsx(_components.span, { className: "token string", children: "\"green\"" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["head", _jsx(_components.span, { className: "token punctuation", children: "(" }), "ball", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# A tibble: 6 × 7" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: " Group_name Thrower Attempt Species Bucket Distance Success\n" }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token operator", children: "<" }), "chr", _jsx(_components.span, { className: "token operator", children: ">" }), " ", _jsx(_components.span, { className: "token operator", children: "<" }), "chr", _jsx(_components.span, { className: "token operator", children: ">" }), " ", _jsx(_components.span, { className: "token operator", children: "<" }), "dbl", _jsx(_components.span, { className: "token operator", children: ">" }), " ", _jsx(_components.span, { className: "token operator", children: "<" }), "chr", _jsx(_components.span, { className: "token operator", children: ">" }), " ", _jsx(_components.span, { className: "token operator", children: "<" }), "dbl", _jsx(_components.span, { className: "token operator", children: ">" }), " ", _jsx(_components.span, { className: "token operator", children: "<" }), "dbl", _jsx(_components.span, { className: "token operator", children: ">" }), " ", _jsx(_components.span, { className: "token operator", children: "<" }), "dbl", _jsx(_components.span, { className: "token operator", children: ">" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "1" }), " BY Yilong Yang ", _jsx(_components.span, { className: "token number", children: "1" }), " teal ", _jsx(_components.span, { className: "token number", children: "5" }), " ", _jsx(_components.span, { className: "token number", children: "2" }), " ", _jsx(_components.span, { className: "token number", children: "0" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "2" }), " BY Yilong Yang ", _jsx(_components.span, { className: "token number", children: "2" }), " yellow ", _jsx(_components.span, { className: "token number", children: "5" }), " ", _jsx(_components.span, { className: "token number", children: "0.5" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "3" }), " BY Yilong Yang ", _jsx(_components.span, { className: "token number", children: "3" }), " green ", _jsx(_components.span, { className: "token number", children: "1" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), " ", _jsx(_components.span, { className: "token number", children: "0" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "4" }), " BY Yilong Yang ", _jsx(_components.span, { className: "token number", children: "4" }), " orange ", _jsx(_components.span, { className: "token number", children: "5" }), " ", _jsx(_components.span, { className: "token number", children: "0.5" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "5" }), " BY Yilong Yang ", _jsx(_components.span, { className: "token number", children: "5" }), " darkpink ", _jsx(_components.span, { className: "token number", children: "5" }), " ", _jsx(_components.span, { className: "token number", children: "0.5" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token number", children: "6" }), " BY Yilong Yang ", _jsx(_components.span, { className: "token number", children: "6" }), " orange ", _jsx(_components.span, { className: "token number", children: "5" }), " ", _jsx(_components.span, { className: "token number", children: "2" }), " ", _jsx(_components.span, { className: "token number", children: "1" }), " \n"] })] }) }), "\n", _jsxs(_components.p, { children: ["考虑模型：", _jsx(_components.code, { className: "language-auto", children: "number_of_species ~ Distance + Bucket" })] }), "\n", _jsxs(_components.p, { children: ["安装", _jsx(_components.code, { className: "language-auto", children: "fitdistrplus" }), " - 用于判断数据是否服从某一分布"] }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["install.packages", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "'fitdistrplus'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["library", _jsx(_components.span, { className: "token punctuation", children: "(" }), "fitdistrplus", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["library", _jsx(_components.span, { className: "token punctuation", children: "(" }), "tidyverse", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: ["fit_pois ", _jsx(_components.span, { className: "token operator", children: "<-" }), " grouped", _jsx(_components.span, { className: "token operator", children: "$" }), "Species_count ", _jsx(_components.span, { className: "token percent-operator operator", children: "%>%" }), " fitdist", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "'pois'" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " method ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token string", children: "\"mle\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["plot", _jsx(_components.span, { className: "token punctuation", children: "(" }), "fit_pois", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Data-Analysis/fitdist.png", alt: "fitdist|500", className: "internal" }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["gofstat", _jsx(_components.span, { className: "token punctuation", children: "(" }), "fit_pois", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["Chi", _jsx(_components.span, { className: "token operator", children: "-" }), "squared statistic", _jsx(_components.span, { className: "token operator", children: ":" }), " ", _jsx(_components.span, { className: "token number", children: "2.988494" }), " \n"] }), _jsxs(_components.span, { className: "code-line", children: ["Degree of freedom of the Chi", _jsx(_components.span, { className: "token operator", children: "-" }), "squared distribution", _jsx(_components.span, { className: "token operator", children: ":" }), " ", _jsx(_components.span, { className: "token number", children: "3" }), " \n"] }), _jsxs(_components.span, { className: "code-line", children: ["Chi", _jsx(_components.span, { className: "token operator", children: "-" }), "squared p", _jsx(_components.span, { className: "token operator", children: "-" }), "value", _jsx(_components.span, { className: "token operator", children: ":" }), " ", _jsx(_components.span, { className: "token number", children: "0.3934026" }), " \n"] }), _jsxs(_components.span, { className: "code-line", children: [" the p", _jsx(_components.span, { className: "token operator", children: "-" }), "value may be wrong with some theoretical counts ", _jsx(_components.span, { className: "token operator", children: "<" }), " ", _jsx(_components.span, { className: "token number", children: "5" }), " \n"] }), _jsxs(_components.span, { className: "code-line", children: ["Chi", _jsx(_components.span, { className: "token operator", children: "-" }), "squared table", _jsx(_components.span, { className: "token operator", children: ":" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: " obscounts theocounts\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "<=" }), " ", _jsx(_components.span, { className: "token number", children: "3" }), " ", _jsx(_components.span, { className: "token number", children: "5.000000" }), " ", _jsx(_components.span, { className: "token number", children: "3.151330" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "<=" }), " ", _jsx(_components.span, { className: "token number", children: "4" }), " ", _jsx(_components.span, { className: "token number", children: "4.000000" }), " ", _jsx(_components.span, { className: "token number", children: "2.676861" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "<=" }), " ", _jsx(_components.span, { className: "token number", children: "5" }), " ", _jsx(_components.span, { className: "token number", children: "3.000000" }), " ", _jsx(_components.span, { className: "token number", children: "3.127701" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "<=" }), " ", _jsx(_components.span, { className: "token number", children: "7" }), " ", _jsx(_components.span, { className: "token number", children: "3.000000" }), " ", _jsx(_components.span, { className: "token number", children: "5.587036" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: ">" }), " ", _jsx(_components.span, { className: "token number", children: "7" }), " ", _jsx(_components.span, { className: "token number", children: "4.000000" }), " ", _jsx(_components.span, { className: "token number", children: "4.457072" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: ["Goodness", _jsx(_components.span, { className: "token operator", children: "-" }), "of", _jsx(_components.span, { className: "token operator", children: "-" }), "fit criteria\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token operator", children: "-" }), "mle", _jsx(_components.span, { className: "token operator", children: "-" }), "pois\n"] }), _jsxs(_components.span, { className: "code-line", children: ["Akaike’s Information Criterion ", _jsx(_components.span, { className: "token number", children: "99.41076" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["Bayesian Information Criterion ", _jsx(_components.span, { className: "token number", children: "100.35520" }), "\n"] })] }) }), "\n", _jsx(_components.p, { children: "可见p值0.39 > 0.05，观测值和预期值之间没有显著差异，符合泊松分布" }), "\n", _jsx(_components.p, { children: "检验其他潜在分布模型：" }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["fit_nbinom ", _jsx(_components.span, { className: "token operator", children: "<-" }), " fitdist", _jsx(_components.span, { className: "token punctuation", children: "(" }), "grouped", _jsx(_components.span, { className: "token operator", children: "$" }), "number_of_species", _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" dist ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token string", children: "'nbinom'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "##plot it out:" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["plot", _jsx(_components.span, { className: "token punctuation", children: "(" }), "fit_nbinom", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Data-Analysis/fitdist1.png", alt: "fitdist1|500", className: "internal" }), "\n", _jsxs(_components.p, { children: ["安装", _jsx(_components.code, { className: "language-auto", children: "glmmTMB" })] }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["install.packages", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "'glmmTMB'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["library", _jsx(_components.span, { className: "token punctuation", children: "(" }), "glmmTMB", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# 泊松分布模型" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["m_mod1 ", _jsx(_components.span, { className: "token operator", children: "<-" }), " glmmTMB", _jsx(_components.span, { className: "token punctuation", children: "(" }), "Count ", _jsx(_components.span, { className: "token operator", children: "~" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Bucket ", _jsx(_components.span, { className: "token operator", children: "+" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Distance ", _jsx(_components.span, { className: "token operator", children: "+" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "# Bucket:Distance + 数据较小，可以不用此行" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token operator", children: "|" }), "Group_name", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" data ", _jsx(_components.span, { className: "token operator", children: "=" }), " grouped", _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" family ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token string", children: "\"poisson\"" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" control", _jsx(_components.span, { className: "token operator", children: "=" }), "glmmTMBControl", _jsx(_components.span, { className: "token punctuation", children: "(" }), "optimizer", _jsx(_components.span, { className: "token operator", children: "=" }), "optim", _jsx(_components.span, { className: "token punctuation", children: "," }), "optArgs", _jsx(_components.span, { className: "token operator", children: "=" }), "list", _jsx(_components.span, { className: "token punctuation", children: "(" }), "method", _jsx(_components.span, { className: "token operator", children: "=" }), _jsx(_components.span, { className: "token string", children: "\"BFGS\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# 负二项分布模型" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["m_mod2 ", _jsx(_components.span, { className: "token operator", children: "<-" }), " glmmTMB", _jsx(_components.span, { className: "token punctuation", children: "(" }), "Count ", _jsx(_components.span, { className: "token operator", children: "~" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Bucket ", _jsx(_components.span, { className: "token operator", children: "+" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" Distance ", _jsx(_components.span, { className: "token operator", children: "+" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token comment", children: "#Bucket:Distance +" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" ", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token number", children: "1" }), _jsx(_components.span, { className: "token operator", children: "|" }), "Group_name", _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" data ", _jsx(_components.span, { className: "token operator", children: "=" }), " grouped", _jsx(_components.span, { className: "token punctuation", children: "," }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [" family ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token string", children: "\"nbinom1\"" }), _jsx(_components.span, { className: "token punctuation", children: "," }), " control", _jsx(_components.span, { className: "token operator", children: "=" }), "glmmTMBControl", _jsx(_components.span, { className: "token punctuation", children: "(" }), "optimizer", _jsx(_components.span, { className: "token operator", children: "=" }), "optim", _jsx(_components.span, { className: "token punctuation", children: "," }), " optArgs", _jsx(_components.span, { className: "token operator", children: "=" }), "list", _jsx(_components.span, { className: "token punctuation", children: "(" }), "method", _jsx(_components.span, { className: "token operator", children: "=" }), _jsx(_components.span, { className: "token string", children: "\"BFGS\"" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsxs(_components.p, { children: ["使用MuMIn 下面的 ", _jsx(_components.code, { className: "language-auto", children: "r.squaredGLMM()" }), " 函数来求其 R2 (R2即拟合度，一般来说，", _jsx(_components.em, { children: "R" }), "-", _jsx(_components.em, { children: "Squared" }), " 越大，表示模型拟合效果越好)"] }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["install.packages", _jsx(_components.span, { className: "token punctuation", children: "(" }), _jsx(_components.span, { className: "token string", children: "'MuMIn'" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["library", _jsx(_components.span, { className: "token punctuation", children: "(" }), "MuMIn", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["r.squaredGLMM", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod1", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: " R2m R2c\n" }), _jsxs(_components.span, { className: "code-line", children: ["delta ", _jsx(_components.span, { className: "token number", children: "0.4912718" }), " ", _jsx(_components.span, { className: "token number", children: "0.5406309" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["lognormal ", _jsx(_components.span, { className: "token number", children: "0.5092221" }), " ", _jsx(_components.span, { className: "token number", children: "0.5603847" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["trigamma ", _jsx(_components.span, { className: "token number", children: "0.4717288" }), " ", _jsx(_components.span, { className: "token number", children: "0.5191244" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: "\n" }), _jsxs(_components.span, { className: "code-line", children: ["r.squaredGLMM", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod2", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), _jsx(_components.span, { className: "token operator", children: "-" }), "\n"] }), _jsx(_components.span, { className: "code-line", children: " R2m R2c\n" }), _jsxs(_components.span, { className: "code-line", children: ["delta ", _jsx(_components.span, { className: "token number", children: "0.4911331" }), " ", _jsx(_components.span, { className: "token number", children: "0.5400752" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["lognormal ", _jsx(_components.span, { className: "token number", children: "0.5091479" }), " ", _jsx(_components.span, { className: "token number", children: "0.5598852" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["trigamma ", _jsx(_components.span, { className: "token number", children: "0.4715176" }), " ", _jsx(_components.span, { className: "token number", children: "0.5185050" }), "\n"] })] }) }), "\n", _jsxs(_components.h3, { id: "评估-glmm-模型的拟合度", children: [_jsx(_components.a, { className: "heading-link", href: "#评估-glmm-模型的拟合度", children: _jsx(_components.svg, { xmlns: "http:www.w3.org/2000/svg", fill: "#ab2b65", viewBox: "0 0 20 20", className: "w-5 h-5", children: _jsx(_components.path, { fillRule: "evenodd", clipRule: "evenodd", d: "M9.493 2.853a.75.75 0 00-1.486-.205L7.545 6H4.198a.75.75 0 000 1.5h3.14l-.69 5H3.302a.75.75 0 000 1.5h3.14l-.435 3.148a.75.75 0 001.486.205L7.955 14h2.986l-.434 3.148a.75.75 0 001.486.205L12.456 14h3.346a.75.75 0 000-1.5h-3.14l.69-5h3.346a.75.75 0 000-1.5h-3.14l.435-3.147a.75.75 0 00-1.486-.205L12.045 6H9.059l.434-3.147zM8.852 7.5l-.69 5h2.986l.69-5H8.852z" }) }) }), "评估 GLMM 模型的拟合度"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.code, { className: "language-auto", children: "DHARMa" }), "包能提供更稳健的方式评估："] }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: [_jsx(_components.span, { className: "token comment", children: "# simulateResiduals方法创建模拟残差" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["m_mod1_sim ", _jsx(_components.span, { className: "token operator", children: "<-" }), " simulateResiduals", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod1", _jsx(_components.span, { className: "token punctuation", children: "," }), " n ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token number", children: "1000" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["m_mod2_sim ", _jsx(_components.span, { className: "token operator", children: "<-" }), " simulateResiduals", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod2", _jsx(_components.span, { className: "token punctuation", children: "," }), " n ", _jsx(_components.span, { className: "token operator", children: "=" }), " ", _jsx(_components.span, { className: "token number", children: "1000" }), _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["plot", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod1_sim", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["plot", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod2_sim", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) }), "\n", _jsxs(_components.p, { children: [_jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Data-Analysis/m_mod1_sim.png", alt: "m_mod1_sim|500", className: "internal" }), "\n", _jsx(_components.img, { src: "https://github.com/Cafwell/picx-images-hosting/raw/master/Data-Analysis/m_mod2_sim.png", alt: "m_mod2_sim|500", className: "internal" })] }), "\n", _jsx(_components.pre, { className: "language-r", children: _jsxs(_components.code, { className: "language-R code-highlight", children: [_jsxs(_components.span, { className: "code-line", children: ["testDispersion", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod1", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] }), _jsxs(_components.span, { className: "code-line", children: ["testDispersion", _jsx(_components.span, { className: "token punctuation", children: "(" }), "m_mod2", _jsx(_components.span, { className: "token punctuation", children: ")" }), "\n"] })] }) })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = { ..._provideComponents(), ...props.components }; return MDXLayout ? _jsx(MDXLayout, { ...props, children: _jsx(_createMdxContent, { ...props }) }) : _createMdxContent(props); } return { default: MDXContent };